Question

Find the limit of (1-x)^(lnx) as x--> 1

Answer 1

let y = (1-x)^lnx
lny = lnx ln(1-x)

Answer 2

yeah that is right

Answer 3

then rewrite as
\[\frac{\ln(1-x)}{\frac{1}{\ln(x)}}\] and use l'hopital

Answer 4

ahhh LH...a very frustrating method involving so much manipulation and circling

Answer 5

LH is frustrating?! it's makes your life easy.

Answer 6

thanks guys you nailed it =]

Answer 7

it's frustating when it circles

Answer 8

if it circles then you are missing some thing

Answer 9

derivative of numerator is
\[-\frac{1}{1-x}\] derivative of denominator is
\[-\frac{1}{x\ln^2(x)}\] ratio is
\[\frac{x\ln^2(x)}{1-x}\]

Answer 10

also... 0/0 is easy.... i hate (inf - inf) 1^inf and something

Answer 11

x goes to one, get 0/1 so not so bad. limit of the log is 0, limit of the original one is
\[e^0=1\] unless i made a mistake

Answer 12

yes you are right 1 is the answer ! =]